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Vertical Limit 
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2 points are said to be colinear if they lie on the same line.
---A---->----B---> Here in this diagram, points A and B lie on the same line and hence are colinear. Thus when 2 vectors act along the same line, then they are said to be colinear.
When 2 vectors act along the same line but have a seperation between them, they are said to be Parallel. i.e Parallel vectors have the same phase, but different magnitudes. That is why when 2 vectors A and B are parallel, then, A=kB, where, K is a constant.
--------A---------> Here A and B are parallel.
----------B--------->
Note: Colinear Vectors are also Parallel vectors except that they lie on the same line.
Mathematically speaking, when 2 vectors are parallel, the dot product of the vectors are 1 and their cross product is zero.(As angle between them is zero)
2 vectors are said to be Co planar if they act in the same plane but they have diferent/same magnitudes and phases.